I believe not. The CMP (a federally chartered non-profit 501(c)(3) corporation, actually called the Corporation for the Promotion of Rifle Practice & Firearms Safety, - not the Army) requires that the 1911 go to an individual, not to another FFL (though I’m not sure if they would consider an 03 an FFL or an individual, since an 03 is “not in the business of manufacturing or selling firearms"). In any case, the CMP has already stated that they will not ship 1911s to MA, period. So it would have to go to an out of state FFL who would then have to transfer it to a MA FFL, which is a CMP no-no (not going direct to an individual).
Right now, I think the only way for a MA resident to get a CMP 1911 is to buy it off an individual from out of state (or from an FFL who bought it from an individual) and have it shipped to a MA FFL. The new law will allow that FFL to transfer it to you even though it is “off list”. You still can’t get one direct from the CMP.
ETA This only works if you nave an 03 (C&R) FFL yourself. If you just have your LTC, a MA FFL still can’t transfer a CMP 1911 to you, since it is “off list”.